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    <title>fstabst</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>fstabst</b> -  Youla's parametrization</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[J]=fstabst(P,r)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>P</b>
        </tt>: <tt>
          <b>syslin</b>
        </tt> list (linear system)</li>
      <li>
        <tt>
          <b>r</b>
        </tt>: 1x2 row vector, dimension of <tt>
          <b>P22</b>
        </tt>
      </li>
      <li>
        <tt>
          <b>J</b>
        </tt>: <tt>
          <b>syslin</b>
        </tt> list (linear system in state-space representation)</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    Parameterization of all stabilizing feedbacks.</p>
    <p>
      <tt>
        <b>P</b>
      </tt> is partitioned as follows:</p>
    <pre>

P=[ P11 P12;
    P21 P22]  
   
    </pre>
    <p>
    (in state-space or transfer form: automatic conversion in state-space is
    done for the computations)</p>
    <p>
      <tt>
        <b>r</b>
      </tt> = size of  <tt>
        <b>P22</b>
      </tt> subsystem, (2,2) block of <tt>
        <b>P</b>
      </tt>
    </p>
    <pre>

          J =[ J11 J12;
               J21 J22]
   
    </pre>
    <p>
      <tt>
        <b>K</b>
      </tt> is a stabilizing controller for <tt>
        <b>P</b>
      </tt> (i.e. <tt>
        <b>P22</b>
      </tt>) iff 
    <tt>
        <b>K=lft(J,r,Q)</b>
      </tt> with <tt>
        <b>Q</b>
      </tt> stable.</p>
    <p>
    The central part of <tt>
        <b>J</b>
      </tt> , <tt>
        <b>J11</b>
      </tt> is the lqg regulator for <tt>
        <b>P</b>
      </tt>
    </p>
    <p>
    This <tt>
        <b>J</b>
      </tt> is such that defining <tt>
        <b>T</b>
      </tt> as the 2-port <tt>
        <b>lft</b>
      </tt> of <tt>
        <b>P</b>
      </tt>
    and <tt>
        <b>J</b>
      </tt> : <tt>
        <b>[T,rt]=lft(P,r,J,r)</b>
      </tt> one has that <tt>
        <b>T12</b>
      </tt> is inner
    and <tt>
        <b>T21</b>
      </tt> is co-inner.</p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

ny=2;nu=3;nx=4;
P22=ssrand(ny,nu,nx);
bigQ=rand(nx+nu,nx+nu);bigQ=bigQ*bigQ';
bigR=rand(nx+ny,nx+ny);bigR=bigR*bigR';
[P,r]=lqg2stan(P22,bigQ,bigR);
J=fstabst(P,r);
Q=ssrand(nu,ny,1);Q('A')=-1;  //Stable Q
K=lft(J,r,Q);
A=h_cl(P,r,K); spec(A)
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="../control/obscont.htm">
        <tt>
          <b>obscont</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="lft.htm">
        <tt>
          <b>lft</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../control/lqg.htm">
        <tt>
          <b>lqg</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../control/lqg2stan.htm">
        <tt>
          <b>lqg2stan</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
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